Get them some cafiza. It’s for cleaning espresso machines but works great for cleaning all oily metal coffee equipment. Just get a big bowl or bucket, fill it with enough hot water to cover the parts, add a teaspoon of cafiza and let it soak for a couple hours. All the gunk should just rinse off, no need to scrub. But don’t soak the gasket.
If you have powdered oxyclean, it’s basically the same thing.
As others have said, the filter is supposed to come out. You just needs a new gasket and they’re cheap and easy to find.